arXiv subjects

Filip Ficek

Publications and source records attributed to Filip Ficek.

28 records · Page 2Linked to original sources

arXiv2021

Ground state in the energy super-critical Gross-Pitaevskii equation with a harmonic potential

The energy super-critical Gross--Pitaevskii equation with a harmonic potential is revisited in the particular case of cubic focusing nonlinearity and dimension d > 4. In order to prove the existence of a ground state (a positive, radially symmetric solution in the energy space), we develop the shooting method and deal with a one-parameter family of classical solutions to an initial-value problem for the stationary equation. We prove that the solution curve (the graph of the eigenvalue parameter versus the supremum) is oscillatory for d <= 12 and monotone for d >= 13. Compared to the existing literature, rigorous asymptotics are derived by constructing three families of solutions to the stationary equation with functional-analytic rather than geometric methods.

math-ph↗

arXiv2021

Schrödinger-Newton-Hooke system in higher dimensions. Part I: Stationary states

The Schrödinger equation with a harmonic potential coupled to the Poisson equation, called the Schrödinger-Newton-Hooke (SNH) system, has been considered in a variety of physical contexts, ranging from quantum mechanics to general relativity. Our work is directly motivated by the fact that the SNH system describes the nonrelativistic limit of the Einstein-massive-scalar system with negative cosmological constant. With this paper we begin the investigations aiming at understanding solutions of the SNH system in the energy supercritical spatial dimensions $d\geq 7$, where we expect to observe interesting short wavelength behaviours due to the confinement of waves by the trapping potential. Here we study stationary solutions and prove existence of one-parameter families of nonlinear ground and excited states. The frequency of the ground state as the function of the central density is shown to exhibit different qualitative behaviours in dimensions $7\leq d\leq 15$ and $d\geq 16$, which is expected to affect the stability properties of the ground states in these dimensions. Our results bear many similarities to the analogous problem that has been studied for the Gross-Pitaevskii equation.

math-ph↗

arXiv2019

Revisiting spin-dependent forces mediated by new bosons: Potentials in the coordinate-space representation for macroscopic- and atomic-scale experiments

The exchange of spin-0 or spin-1 bosons between fermions or spin-polarised macroscopic objects gives rise to various spin-dependent potentials. We derive the coordinate-space non-relativistic potentials induced by the exchange of such bosons, including contact terms that can play an important role in atomic-scale phenomena, and correct for errors and omissions in the literature. We summarise the properties of the potentials and their relevance for various types of experiments. These potentials underpin the interpretation of experiments that search for new bosons, including spectroscopy, torsion-pendulum measurements, magnetometry, parity nonconservation and electric dipole moment experiments.

hep-ph↗

arXiv2018

A nonrelativistic limit for AdS perturbations

The familiar $c\rightarrow \infty$ nonrelativistic limit converts the Klein-Gordon equation in Minkowski spacetime to the free Schroedinger equation, and the Einstein-massive-scalar system without a cosmological constant to the Schroedinger-Newton (SN) equation. In this paper, motivated by the problem of stability of Anti-de Sitter (AdS) spacetime, we examine how this limit is affected by the presence of a negative cosmological constant $Λ$. Assuming for consistency that the product $Λc^2$ tends to a negative constant as $c\rightarrow \infty$, we show that the corresponding nonrelativistic limit is given by the SN system with an external harmonic potential which we call the Schrodinger-Newton-Hooke (SNH) system. We then derive the resonant approximation which captures the dynamics of small amplitude spherically symmetric solutions of the SNH system. This resonant system turns out to be much simpler than its general-relativistic version, which makes it amenable to analytic methods. Specifically, in four spatial dimensions, we show that the resonant system possesses a three-dimensional invariant subspace on which the dynamics is completely integrable and hence can be solved analytically. The evolution of the two-lowest-mode initial data (an extensively studied case for the original general-relativistic system), in particular, is described by this family of solutions.

gr-qc↗

arXiv2018

Constraining exotic interactions

Beyond-the-standard-model interactions mediated by an exchange of virtual "new" bosons result in a finite set of possible effective interaction potentials between standard-model particles such as electrons and nucleons. We discuss the classification of such potentials and briefly review recent experiments searching for such exotic interactions at spatial scales from sub-nanometers to tens of thousand kilometers.

hep-ph↗

arXiv2018

Constraints on exotic spin-dependent interactions between matter and antimatter from antiprotonic helium spectroscopy

Heretofore undiscovered spin-0 or spin-1 bosons can mediate exotic spin-dependent interactions between standard-model particles. Here we carry out the first search for semileptonic spin-dependent interactions between matter and antimatter. We compare theoretical calculations and spectroscopic measurements of the hyperfine structure of antiprotonic helium to constrain exotic spin- and velocity-dependent interactions between electrons and antiprotons.

physics.atom-ph↗

arXiv2017

Planar domain walls in black hole spacetimes

We investigate the behaviour of low-mass, planar domain walls in the so-called $ϕ^4$ model of the scalar field on the Schwarzschild and Kerr backgrounds. We focus on a transit of a domain wall through a black hole and solve numerically the equations of motion for a range of parameters of the domain wall and the black hole. We observe a behavior resembling an occurrence of ringing modes. Perturbations of domain walls vanish during latter evolution, suggesting their stability against a passage through the black hole. The results obtained for Kerr and Reissner-Nordström black holes are also compared.

gr-qc↗

arXiv2017

Constraints on exotic spin-dependent interactions between electrons from helium fine-structure spectroscopy

Agreement between theoretical calculations of atomic structure and spectroscopic measurements is used to constrain possible contribution of exotic spin-dependent interactions between electrons to the energy differences between states in helium-4. In particular, constraints on dipole-dipole interactions associated with the exchange of pseudoscalar bosons (such as axions or axion-like particles, ALPs) with masses $10^{-2}~{\rm eV} \lesssim m \lesssim 10^{4}~{\rm eV}$ are improved by a factor of $\sim 100$. The first atomic-scale constraints on several exotic velocity-dependent dipole-dipole interactions are established as well.

physics.atom-ph↗

arXiv2015

Bondi-type accretion in the Reissner-Nordström-(anti-)de Sitter spacetime

In this paper I study stationary, spherically symmetric accretion of fluids onto a charged black hole in the presence of the cosmological constant. For some isothermal equations of state it is possible to obtain analytic solutions. In the case of a radiation fluid I point out a connection between locations of the horizons and the sonic (critical) points. In specific cases the solutions form closed, binoculars-like trajectories in a phase diagram of the velocity vs. radius.

gr-qc↗

arXiv2015

Evolutionary tracks of millisecond pulsars with low-mass companions

We consider the evolution of millisecond radio pulsars in binary systems with a main-sequence or evolved stellar companion. Evolution of non-accreting binary systems with "eclipsing" milisecond pulsars was described by Kluźniak, Czerny & Ray (1992) who predicted that systems like the one containing the Terzan 5 PSR 1744-24A will in the future become accreting low mass X-ray binaries (LMXBs), while PSR 1957+20 may evaporate its companion. The model presented in the current paper gives similar results for these two objects and allows to obtain diverse evolutionary tracks of millisecond pulsars with low mass companions (black widows). Our results suggest that the properties of many black widow systems can be explained by an ablation phase lasting a few hundred million years. Some of these sources may regain Roche lobe contact in a comparable time, and become LMXBs.

astro-ph.HE↗